MinT - Information on Result #869276

Information on Result #869276

Linear OOA(32⁴⁶, 16418, F₃₂, 2, 13) (dual of [(16418, 2), 32790, 14]-NRT-code), using OOA 2-folding based on linear OA(32⁴⁶, 32836, F₃₂, 13) (dual of [32836, 32790, 14]-code), using

discarding factors / shortening the dual code based on linear OA(32⁴⁶, 32837, F₃₂, 13) (dual of [32837, 32791, 14]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(32⁹, 66, F₃₂, 6) (dual of [66, 57, 7]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(32³, 33, F₃₂, 3) (dual of [33, 30, 4]-code or 33-arc in PG(2,32) or 33-cap in PG(2,32)), using
        extended Reedâ€“Solomon code RS_e(30,32) [i]
      2. linear OA(32⁶, 33, F₃₂, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
        extended Reedâ€“Solomon code RS_e(27,32) [i]
  2. linear OA(32³⁷, 32771, F₃₂, 13) (dual of [32771, 32734, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(32³⁷, 32768, F₃₂, 13) (dual of [32768, 32731, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(32³⁴, 32768, F₃₂, 12) (dual of [32768, 32734, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.